A Great Tool to Use in Finding the Sine and Cosine of Certain Angles UNIT CIRCLE A Great Tool to Use in Finding the Sine and Cosine of Certain Angles
Start with the Coordinate Plane
Draw a Circle whose center is at the origin
Whose Radius is one unit 1
1 Pick a point (x, y) on the circle and draw the terminal side of an angle through the point
Because the Radius is one unit 1
1
1
1
1
1
1
1
1
1
Every point (x, y) on the circle will have the coordinates 1 Every point (x, y) on the circle will have the coordinates
Every point (x, y) on the circle will have the coordinates
Every point (x, y) on the circle will have the coordinates
Every point (x, y) on the circle will have the coordinates
1
1
1
1
1
1
1
1
1 Which We Saw in the Past
and
1 Pythagoras
1 Pythagoras
1 Pythagoras
1 Pythagoras
1 Pythagoras
1 Pythagoras
1 Pythagoras
1 Pythagoras
1 Pythagoras
The Big 2 1 Pythagoras
Now
Recall Radian Degree Circle
Writing them INSIDE the circle Degrees Writing them INSIDE the circle
Writing them INSIDE the circle Radians Writing them INSIDE the circle
Next
Put the Circle in the Coordinate Plane
Let the Circle have a radius of 1
1
What are the coordinates of 1 What are the coordinates of
What are the coordinates of 1 What are the coordinates of
What are the coordinates of 1 What are the coordinates of
What are the coordinates of 1 What are the coordinates of
Remember The Quadrantals
If we made an ordered pair (cosine, sine) It would be (1,0) which were the coordinates of the point that the terminal side passes through when
Same as it's Coordinates!
If we made an ordered pair (cosine, sine) It would be (0,1) which were the coordinates of the point that the terminal side passes through when
Same as it's Coordinates!
If we made an ordered pair (cosine, sine) It would be (–1,0) which were the coordinates of the point that the terminal side passes through when
Same as it's Coordinates!
If we made an ordered pair (cosine, sine) It would be (0,–1 ) which were the coordinates of the point that the terminal side passes through when
Same as it's Coordinates!
They are the same as the Coordinates! You Now Have An Easy Way To Remember The Cosine and Sine for the Quadrantal Angles They are the same as the Coordinates!
Angles Whose Reference Angle is
Writing them INSIDE the circle Degrees Writing them INSIDE the circle
Writing them INSIDE the circle Radians Writing them INSIDE the circle
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From The Special Angles Remember From The Special Angles
We know that we can find the tangent, secant, cosecant and cotangent Quadrant Angle I We know that we can find the tangent, secant, cosecant and cotangent When we know just the Cosine and Sine II III IV
Quadrant Angle And we can determine if they are Positive or Negative in each Quadrant using the Table Below I II III IV
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Angles Whose Reference Angle is
Writing them INSIDE the circle Degrees Writing them INSIDE the circle
Writing them INSIDE the circle Radians Writing them INSIDE the circle
?
From The Special Angles Remember From The Special Angles
We know that we can find the tangent, secant, cosecant and cotangent Quadrant Angle I We know that we can find the tangent, secant, cosecant and cotangent When we know just the Cosine and Sine II III IV
Quadrant Angle And we can determine if they are Positive or Negative in each Quadrant using the Table Below I II III IV
?
?
?
Angles Whose Reference Angle is
Writing them INSIDE the circle Degrees Writing them INSIDE the circle
Writing them INSIDE the circle Radians Writing them INSIDE the circle
?
From The Special Angles Remember From The Special Angles
We know that we can find the tangent, secant, cosecant and cotangent Quadrant Angle I We know that we can find the tangent, secant, cosecant and cotangent When we know just the Cosine and Sine II III IV
Quadrant Angle And we can determine if they are Positive or Negative in each Quadrant using the Table Below I II III IV
?
?
?
?
Sine and Cosine of Angles A Great Tool to Use in Finding the Sine and Cosine of Angles
Remember that we can find the tangent, secant, cosecant and cotangent When we know just the Cosine and Sine THE UNIT CIRCLE And now we have